No. The transformer has only one input of energy -- the primary; output power divided by input power is efficiency and you can never get more out than you put in. In fact, a transformer, although a pretty efficient device, isn't perfect, and there will be losses in the core from eddy currents and poor coupling and resistive losses in both the primary and secondary.
Think about this: a transformer that is 90% efficient running at full load will get warm to the touch. If a transformer was 120% efficient, then would it actually get cool to the touch?
Dean